[prev] [prev-tail] [tail] [up]

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [155] had the largest ratio of [76]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 4 3 1.00 9 0.333
2 A 4 3 1.00 9 0.333
3 A 4 3 1.00 9 0.333
4 A 4 3 1.00 7 0.429
5 A 3 3 1.00 5 0.600
6 A 1 1 1.00 9 0.111
7 A 5 5 1.00 9 0.556
8 A 4 3 1.00 9 0.333
9 A 4 3 1.00 9 0.333
10 A 4 3 1.00 9 0.333
11 A 5 3 1.00 9 0.333
12 A 5 3 1.00 9 0.333
13 A 5 3 1.00 7 0.429
14 A 4 3 1.00 5 0.600
15 A 1 1 1.00 9 0.111
16 A 6 5 1.00 9 0.556
17 A 5 3 1.00 9 0.333
18 A 5 3 1.00 9 0.333
19 A 5 4 1.00 11 0.364
20 A 5 4 1.00 11 0.364
21 A 4 4 1.00 9 0.444
22 A 1 1 1.00 11 0.091
23 A 6 6 1.00 11 0.546
24 A 5 4 1.00 11 0.364
25 A 5 4 1.00 11 0.364
26 A 5 4 1.00 11 0.364
27 A 5 4 1.00 11 0.364
28 A 4 4 1.00 7 0.571
29 A 3 3 1.00 11 0.273
30 A 4 4 1.00 11 0.364
31 A 5 4 1.00 11 0.364
32 A 6 4 1.00 11 0.364
33 A 6 4 1.00 11 0.364
34 A 5 4 1.00 9 0.444
35 A 1 1 1.00 11 0.091
36 A 7 6 1.00 11 0.546
37 A 6 4 1.00 11 0.364
38 A 6 4 1.00 11 0.364
39 A 6 4 1.00 11 0.364
40 A 6 4 1.00 11 0.364
41 A 5 4 1.00 7 0.571
42 A 4 3 1.00 11 0.273
43 A 5 4 1.00 11 0.364
44 A 6 4 1.00 11 0.364
45 A 3 3 1.00 11 0.273
46 A 3 3 1.00 9 0.333
47 A 3 3 1.00 7 0.429
48 A 1 1 1.00 11 0.091
49 A 3 3 1.00 11 0.273
50 A 3 3 1.00 11 0.273
51 A 3 3 1.00 11 0.273
52 A 4 3 1.00 11 0.273
53 A 4 3 1.00 9 0.333
54 A 4 3 1.00 7 0.429
55 A 1 1 1.00 11 0.091
56 A 4 3 1.00 11 0.273
57 A 4 3 1.00 11 0.273
58 A 4 3 1.00 11 0.273
59 A 7 5 1.00 13 0.385
60 A 6 5 1.00 13 0.385
61 A 5 5 1.00 13 0.385
62 A 4 4 1.00 13 0.308
63 A 5 5 1.00 13 0.385
64 A 6 5 1.00 13 0.385
65 A 9 5 1.00 13 0.385
66 A 8 5 1.00 13 0.385
67 A 7 5 1.00 13 0.385
68 A 6 5 1.00 13 0.385
69 A 5 4 1.00 13 0.308
70 A 6 5 1.00 13 0.385
71 A 7 5 1.00 13 0.385
72 A 9 8 1.00 15 0.533
73 A 8 8 1.00 15 0.533
74 A 8 8 1.00 15 0.533
75 A 7 7 1.00 15 0.467
76 A 7 7 1.00 15 0.467
77 A 8 8 1.00 15 0.533
78 A 10 8 1.00 15 0.533
79 A 10 8 1.00 15 0.533
80 A 9 8 1.00 15 0.533
81 A 9 8 1.00 15 0.533
82 A 8 7 1.00 15 0.467
83 A 8 7 1.00 15 0.467
84 A 9 8 1.00 15 0.533
85 A 9 8 1.00 15 0.533
86 A 4 4 1.00 15 0.267
87 A 4 4 1.00 15 0.267
88 A 4 4 1.00 15 0.267
89 A 4 4 1.00 15 0.267
90 A 4 4 1.00 15 0.267
91 A 5 4 1.00 15 0.267
92 A 5 4 1.00 15 0.267
93 A 5 4 1.00 15 0.267
94 A 5 4 1.00 15 0.267
95 A 5 4 1.00 15 0.267
96 A 0 0 0.00 0 0.000
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 0 0 0.00 0 0.000
100 A 0 0 0.00 0 0.000
101 A 2 1 1.00 15 0.067
102 A 3 3 1.00 11 0.273
103 A 4 3 1.00 11 0.273
104 A 5 3 1.00 11 0.273
105 A 4 4 1.00 13 0.308
106 A 5 4 1.00 13 0.308
107 A 6 4 1.00 13 0.308
108 A 4 4 1.00 13 0.308
109 A 5 4 1.00 13 0.308
110 A 6 4 1.00 13 0.308
111 A 4 4 1.00 13 0.308
112 A 5 4 1.00 13 0.308
113 A 6 4 1.00 13 0.308
114 A 0 0 0.00 0 0.000
115 A 0 0 0.00 0 0.000
116 A 1 1 1.00 9 0.111
117 A 0 0 0.00 0 0.000
118 A 0 0 0.00 0 0.000
119 A 0 0 0.00 0 0.000
120 A 0 0 0.00 0 0.000
121 A 1 1 1.00 11 0.091
122 A 0 0 0.00 0 0.000
123 A 0 0 0.00 0 0.000
124 A 13 8 1.00 13 0.615
125 A 10 8 1.00 11 0.727
126 A 7 7 1.00 9 0.778
127 A 3 3 1.00 13 0.231
128 A 7 9 1.00 13 0.692
129 A 11 11 1.00 13 0.846
130 A 14 11 1.00 13 0.846
131 A 33 13 1.00 13 1.000
132 A 19 12 1.00 11 1.091
133 A 9 8 1.00 9 0.889
134 A 0 0 0.00 0 0.000
135 A 6 5 1.00 13 0.385
136 A 12 13 1.00 13 1.000
137 A 16 8 1.00 17 0.471
138 A 13 8 1.00 17 0.471
139 A 10 8 1.00 15 0.533
140 A 7 7 1.00 9 0.778
141 A 3 3 1.00 17 0.176
142 A 8 5 1.00 17 0.294
143 A 12 8 1.00 17 0.471
144 A 15 9 1.00 17 0.529
145 A 5 5 1.00 9 0.556
146 A 5 5 1.00 12 0.417
147 A 8 6 1.00 12 0.500
148 A 8 6 1.00 15 0.400
149 A 1 1 1.00 34 0.029
150 A 1 1 1.00 34 0.029
151 A 1 1 1.00 34 0.029
152 A 1 1 1.00 37 0.027
153 A 2 2 1.00 53 0.038
154 A 2 2 1.00 53 0.038
155 A 4 4 1.00 76 0.053
156 A 5 3 1.00 19 0.158
157 A 4 3 1.00 19 0.158
158 A 3 3 1.00 17 0.176
159 A 2 2 1.00 15 0.133
160 A 0 0 0.00 0 0.000
161 A 38 16 1.00 16 1.000
162 A 31 16 1.00 16 1.000
163 A 22 17 1.00 14 1.214
164 A 15 12 1.00 13 0.923
165 A 1 2 1.00 16 0.125
166 A 10 13 1.00 16 0.812
167 A 23 17 1.00 16 1.062
168 A 30 17 1.00 16 1.062
169 A 37 17 1.00 16 1.062
170 A 25 18 1.00 20 0.900
171 A 21 18 1.00 18 1.000
172 A 18 14 1.00 17 0.824
173 A 3 3 1.00 20 0.150
174 A 12 10 1.00 20 0.500
175 A 20 17 1.00 20 0.850
176 A 28 19 1.00 20 0.950
177 A 108 20 1.00 27 0.741
178 A 67 20 1.00 25 0.800
179 A 42 17 1.00 24 0.708
180 A 0 0 0.00 0 0.000
181 A 22 9 1.00 27 0.333
182 A 44 16 1.00 27 0.593
183 A 78 18 1.00 27 0.667
184 A 52 17 1.00 21 0.810
185 A 40 21 1.00 19 1.105
186 A 26 20 1.00 18 1.111
187 A 18 15 1.00 21 0.714
188 A 13 17 1.00 21 0.810
189 A 30 20 1.00 21 0.952
190 A 41 19 1.00 21 0.905
191 A 51 19 1.00 21 0.905
192 A 60 22 1.00 24 0.917
193 A 43 21 1.00 23 0.913
194 A 29 24 1.00 26 0.923
195 A 19 21 1.00 26 0.808
196 A 32 22 1.00 26 0.846
197 A 43 20 1.00 26 0.769
198 A 61 19 1.00 26 0.731

[prev] [prev-tail] [front] [up]